These are uneasy times for America's Muslims, caught in a backlash from a presidential election campaign where the false notion that Barack Obama is Muslim has been seized on by some who link Islam with terrorism.

The Democratic White House candidate, who would be the first black US president and whose middle name is Hussein, is a Christian.

Son of a Kenyan father and white American mother, he spent part of his childhood in largely Muslim Indonesia.

The idea Obama is Muslim has circulated on the internet for months, presented by some as a fact to reinforce the position many in battleground states where Obama is in a close fight with Republican candidate John McCain.

The film, distributed by a private group unaffiliated with the McCain campaign, features suicide bombers, children being trained with guns, and a Christian church said to have been defiled by Muslims.

• A city council candidate in Irvine, California, who is Muslim convert, said he got a telephone call saying "I want to cut your head off just like all the other Muslims deserve," the Los Angeles Times reported.

• A mosque in a suburb of Chicago, Obama's home city, was vandalized four times in less than two months, with anti-Islamic messages left on its outer walls, and windows and doors broken.

• An account of an Ohio rally for McCain running mate Sarah Palin, filed by Al Jazeera and posted on YouTube, shows a woman saying "he is not Christian, and this is a Christian nation," and a second woman saying she opposes Obama because of "the whole Muslim thing. A lot of people have forgotten about 9/11 (the Sept. 11, 2001, attacks). It's a little unnerving."

"It is frightening to see at this point the label 'Arab' or 'Muslim' being used de facto as an insult," said Ahmed Rehab, executive director of the Chicago office of the Council on American-Islamic Relations (C.A.I.R).

There is a feeling, he said, that hate crimes increase as Islamophobia rises in public discourse, including that going on peripherally in this election campaign.

Former Secretary of State Colin Powell, a Republican crossing party lines to endorse Obama on Sunday, made a demand for tolerance when he referred to Obama-is-a-Muslim rumours.

"Is there something wrong with being a Muslim in this country?" he asked on NBC's "Meet the Press."

"The answer's no, that's not America. Is there something wrong with some seven-year-old Muslim-American kid believing that he or she could be president?

"Yet I have heard senior members of my own party drop the suggestion 'he's a Muslim and he might be associated with terrorists.' This is not the way we should be doing it in America," Powell said, while making clear such sentiment was not coming from McCain himself.

Muslims make up less than 1 percent of the US population of 305 million, according to the Pew Forum on Religion and Public Life, though some believe that number is low. About a third of the world's population is Christian, another 21 percent Muslim.

Daniel Varisco, anthropology chair at Hofstra University, said he wrote the "statement of concerned scholars" after seeing Islamophobia on the rise.

"The attempts to label Senator Obama a terrorist or rhyme his name with Osama (bin Laden) or accent his middle name (Hussein), as well as false claims about his being sworn into (US Senate) office on a Koran, demonstrate how near to the surface anti-Islamic sentiment is in the United States," he said.

Circulating such falsehoods "avoids playing the race card directly but at the expense of Muslims," he said.

The Clarion Fund, which distributed the film "Obsession," through a huge newspaper advertising buy, says it is an independent education group focused "on the most urgent threat of radical Islam" and that placing the film in the hands of readers in battleground election states was an attempt to grab attention.

Spokesman Gregory Ross said, "we have no political or religious affiliations to any group whatsoever."

The Islamic Circle of North America has meanwhile opened an offensive of sorts – a campaign promoting Islam and seeking converts. It said it placed advertising signs inside 1,000 cars in New York's subway network.

In Chicago the group had a number of city buses adorned top to bottom with pro-Islam advertising, headlined "Islam: The Way of Life of Noah, Abraham, Moses, Jesus and Muhammad."

Rehab of the Chicago C.A.I.R. office said that kind of approach may work to a limited degree, "but really the crux of the issue is not learning about the details of a religion but rather interacting with and understanding that the average Muslim is no different than yourself."